Multiplying by the integrating factor allows the left-hand side of the equation to be written as the derivative of $$e^{\int P(x)\,dx} * y$$.

After multiplying by the integrating factor, one can integrate both sides to solve for $$y$$.

Multiplying the entire equation by the integrating factor $$e^{\int P(x)\,dx}$$ eliminates the derivative term from the equation.

The integrating factor is given by $$e^{\int P(x)\,dx}$$.